POLITICS OF THE DAY.; The Four Candidates An Estimate of their Relative Strength, from a Western Point of View The Probable Result. Correspondence of the New-York Times.

The Conventions have all completed their work, and it only remains to record the votes in order to complete a drama in which Farce, Comedy and Tragedy are about equally mixed. The Conventions have ended just about where old and experienced politicians foresaw they would. BATES and SEWARD were laid on the shelf at Chicago, and DOUGLAS was not nominated by the Democratic Party, but has allowed himself to become a wedge separating that once powerful party into two hostile, bitter, irreconcilable and destructive elements. The Southern Democracy were determined to destroy him, and the Northern Democracy were determined to nominate him. They have both succeeded, and the Democratic Party is utterly and irremediably destroyed. I say this advisedly; for to such a party, without a single principle to rest upon, there can be no revival in this generation. The name may be given to another party in other times. In the meanwhile, let us look at the aspect of the field, and let us do it as calmly and fairly as if we had no choice in the matter.

In the first place, you may expect any amount of flags, drums and trumpets displayed by the Douglas men, for that is all they can do; as to the reality, it will be everywhere, like the ratification at Cincinnati -- a few voters and some boys -- making an insignificant parade. In truth, the first thing we remember is that the Douglas part of the Democracy is now in the situation of the Fillmore men in 1856. FILLMORE polled 800,000 votes, but got the electoral vote of but one State. DOUGLAS may get Missouri or some other stray State; but it would puzzle anybody to give a reason for a probability of more than one or two States in his favor. Any cue who is at all familiar with politics knows that the whole South will either go to BRECKINRIDGE or BELL. No State in the Northwest can go to DOUGLAS but Indiana. And what prospect is there there? Every Fillmore paper there is out for LINCOLN. DOUGLAS will meet a united opposition, and that of thousands of Administration Democrats. The probality in Indiana will be against him by thousands. In Illinois the chances for him are hardly worth counting. In the other Northwestern States the majorities against him will be very heavy. On the supposition that all th8 nominees will run as they are now placed, and making due allowance for any possible doubts, which the state of past votes will admit of, I make the following careful analysis of the coming vote. In the first place, as an important element of calculation, I give you the relative votes of the American and Democratic Parties in the South in 1856 as follows, viz.:

It will be observed that the proportion of the majority to the whole vote polled is as follows: Arkansas, 35 per cent.; Texas, 30 per cent.; Virginia, 20; Mississippi, 18; Georgia, 14; North Carolina, 13; Florida, 13; Delaware, 13; Alabama, 12; Missouri, 9; Tennessee, 5; Kentucky, 5; Louisiana, 5. Now, every intelligent person sees by this exhibit that Arkansas, Texas, Virginia, Mississippi, Georgia, North Carolina, Florida and Alabama must go to the Southern candidate, unless there is a very great division of the Democratic vote there; and in that event, they must go to BELL.

So it is evident that Maryland, Kentucky, Tennessee, and Louisiana will go to Bell, with the least division of the Democracy. These are the States where DOUGLAS might expect some strength; but where, if a Douglas ticket is run, they go inevitably to the Opposition. DOUGLAS in the South is where VAN BUREN was in the North. It is a practical sham to run Douglas tickets in the South. The electoral votes of the entire South must go therefore, to one or other of the Southern candidates. Let us now look to the North. What States are there which can in fairness be called doubtful? Put down, if you please, all the Buchanan States of 1856, except California, whic will go to the South. Let us begin with Illinois. LINCOLN beat DOUGLAS 4,000 votes, (with 5,000 Administration votes to spare,) and the aid of some Republicans for DOUGLAS, The Americans go for LINCOLN, -- the Republicans go; and the Administration Democrats will probably run a Breckinridge ticket. There is no probability whatever that Illinois will go for DOUGLAS. The same state of things is found in Indiana. How is it in Pennsylvania and New-Jersey? Is it not evident that the Democratic Party there is divided? How then can LINCOLN fail? In New-York, you see the Hards under DICKINSON for BRECKINRIDGE; and the Douglas ticket will lose quite as many votes which go for BRECKINRIDGE as the Americans poll for BELL -- so that New-York will give a heavy majority for LINCOLN. In Pennsylvania, the same thing will take place. In one word, it is not easy to see how DOUGLAS can get a single State. The chapter of accidents may give hint two or three.

To determine how the South will go, it is only necessary to look at two or three obvious facts. In the State of Kentucky, the Louisville Democrat, and perhaps one or two more papers only, support DOUGLAS. Now suppose the Douglas faction is able to poll 10,000 votes, and probably they will more, what is the consequence? The State goes for BELL. Suppose the Douglas men are able t� poll 20,000 votes in Virginia; then Virginia goes for BELL. In Louisiana the Douglas faction is simply the Soule faction, and it is small. But if they do anything at all, they will give the State to BELL. The same effect will follow a Douglas movement in the greater part of the Southern States. Assuming, then, as a fact, that Douglas tickets will be run in the South, the probability is that BELL will be the next to LINCOLN in the electoral votes. If Douglas tickets are not run in the South, BRECKINRIDGE will be the second highest.

The conclusion of the whole matter is, as you have expressed it in the TIMES, that with due diligence, LINCOLN must be elected, with a Republican House of Representatives. It will be the best thing for the country; for than the threats made by the Southern extremists, of resistance to a Republican Administration, will be found nothing but empty air. The South is divided, and the Conservatives are the strongest.

A VETERAN OBSERVER.

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A version of this archives appears in print on July 9, 1860, on Page 4 of the New York edition with the headline: POLITICS OF THE DAY.; The Four Candidates An Estimate of their Relative Strength, from a Western Point of View The Probable Result. Correspondence of the New-York Times. Order Reprints|Today's Paper|Subscribe